I would always negotiate pay at the end of the interview. I spend the whole interview giving them a reason to hire me, and usually by the time we get to the end/bit about pay, they'll want me enough to not mind discussing it. I'm a bit lucky 'cause I've always interviewed well, but I'd suggest the same strategy for you. I'm not sure what you come off across in person, but I ALWAYS go in to discuss wages - I never do it over the phone 'cause you can't read social cues for what to say/how to say things to the employer.
I usually soften the blow by asking if I can ask a question without hurting my interview and I purposefully say it shyly even though I know what my budging point is/what I want.
Imo, if they don't give you what you think is reasonable...I'd keep looking. If you're good at what you do and you employer can't see you as that asset from the start, then find someone who will. Seeming desperate lowers your value to the company & I would never take a pay cut unless that's what it took to get my foot in the door and I could reasonably expect to move up.
Good luck
You are still in school right?